Question

According to Archimedes' principle, the mass of a floating object equals the mass of the fluid displaced by the object. A 150-lbm swimmer is floating in nearby pool; 95% of her body's volume is in the water while 5% of her body's volume is above water. Determine the density of the swimmer's body The density of water is 0.036 lbm/in5. Does your answer make sense?? Why why not?

Answer 1

Answer:

The density of the swimmer is 0.0342 lbm/in3.

This value makes sense as the density of the body is very similar to the water.

Explanation:

If the swimmers is floating, the weight of the swimmer must be equal to the upward buoyant force.

We can express the weight force as the product of density and volume of the swimmer.

Then

$\rho_{swimmer}*V_{swimmer}=\rho_{water}*V_{water_displaced}\\\\\rho_{swimmer}*V_{swimmer}=\rho_{water}*0.95**V_{swimmer}\\\\\rho_{swimmer}=0.95*\rho_{water}\\\\\rho_{swimmer}=0.95*0.036 lbm/in3\\\\\rho_{swimmer}=0.0342lbm/in3$

It makes sense as the density of the body is very similar to the water.